Many biological parameters and processes can be sensed and monitored using its impedance as marker [1-5], with the advantage of being a non-invasive and relatively cheap technique. Cell growth and activity, changes in cell composition, shape or in cell location are examples of how processes can be detected with microelectrode-cell impedance sensors [6-9]. Among Impedance Spectroscopy (IS) techniques, Electrical Cell-substrate Impedance Spectroscopy (ECIS) [7, 8], based on two-electrode setups, allows the measure of cell-culture impedances and the definition of the biological nature (material, internal activity, motility and size) of a kind of cell and its relationship with the environment [H]. One of the drawbacks of ECIS technique is the need of efficient models to decode the electrical performance of the full system composed by the electrodes, medium and cells. Several works have been developed in this field. In [8], magnitude and phase impedance are deduced from electric field equation solution at the cell-electrode interface, giving a three parameter based model (h, the cellelectrode distance, R^sub b^ cell-to-cell barrier resistance and roeu, cell radius). In [9, 10], finite element simulation (FEM) is executed to solve electrical field considering the whole structure. This method gives one parameter model (R^sub gap^) to describe the gap or cell-electrode region resistance. In both, the model considers cells are in confluent phase [7] or a fixed area over the electrode [9]. The latest was extended in [10] to several cell sizes, allowing to define the cell-electrode covered area as the main model parameter. In this work, an extension of the Rgap based model is considered, to incorporate the cell-microelectrode area overlap variable [10]. Impedance sensor sensitivity curves based on the cell size and density will be presented and applied to measure the growth rate in cell-cultures and to describe cell toxicity experiments.

In this paper, section II summarizes the electrode-solution model and complete cell-electrode characterization. The process to extract practical models is included in section III, illustrating the simulations on a simplified system leading to cell size detection. Section IV describes real time cell culture monitoring and its application to dosimetry experiments. Conclusions are highlighted in section V.

2. Electrode-electrolyte Model

The impedance of electrodes in ionic liquids has been extensively investigated. An excellent review can be found in [6]. The main components describing the electrical performance of an electrode metal inside a solution are four: the double layer capacitance, C^sub l^, the resistance caused by the electron transfer at the electrode surface, R^sub ct^, the Warburg impedance, Z^sub w^, due to limited mass diffusion from the electrode surface to the solution, in series with Ra, and the spreading resistance, Rs, the solution conductivity encountered as the current spreads out to the bulk solution. These four parameters depend on the technology, medium and geometry.

3. Cell-electrode Model

Fig. 2 illustrates a two-electrode impedance sensor useful for ECIS technique: ei is the sensing electrode and e^sub 2^ the reference one. The e^sub 2^ electrode is commonly larger and ground connected, being its resistance small enough to be rejected. Electrodes can be manufactured in CMOS processes with metal layers [9] or using post-processing steps [13]. The cell location and size on e^sub 1^ top must be detected.

The model in Fig. 3 considers the sensing surface of ei can be totally or partially filled by cells. For the two-electrode sensor of Fig. 2, e^sub 1^ defines the sensing area A, and Z(ω) is the impedance by unit area of the empty electrode, without cells on top (Fig 3a). When ei is partially covered by cells in a surface Ac, Z(ω)/ (A-A^sub c^) is the electrode impedance associated to the uncovered area, and Z(ω)/A^sub c^ the impedance of the covered one (Fig 3b). R^sub gap^ models the current flowing laterally in the electrode-cell interface, which depends on the electrode-cell distance at the interface (in the range of 15-150 nm). The Rs is the spreading resistance through the conductive solution. For an empty electrode, the impedance model Z(ω) is represented by the circuit in Fig. 2. It has been considered for e2 the model in Fig 3a, not covered by cells. The e2 electrode is commonly larger and ground connected, being its resistance small enough to be rejected.

Fig. 4 represents the impedance magnitude, Z^sub c^, for the sensor system in Fig. 2, considering that ei could be either empty, partially or totally covered by cells. The parameter ff, fill factor, can be zero for A^sub c^=0 (e^sub 1^ electrode empty), and 1 for A^sub c^=A (e^sub 1^ electrode full). It is defined Z^sub c^ ( ff = 0 ) = Z^sub nc^ as the impedance magnitude of the sensor without cells.

The relative change of the impedance magnitude is defined as

... (1)

which informs more accurately from these variations, being r the change of impedance magnitude for the two-electrode with cells (Z^sub c^) with respect to the system without them (Z^sub nc^). The graphics of r versus frequency are plotted in Fig. 5, for a cell-electrode coverage ff from 0.1 to 0.9 in steps of 0.1, using an R^sub gap^ = 90 kohm. The size of the electrode is 32 × 32 µm^sup 2^, as in [9, 10]. The frequency where the sensitivity to cells is higher can be identified at 100 kHz, represented by r increments, in accordance with previous results [9, 10]. For a given frequency, each normalized impedance value of r can be linked with its ff, being possible the cell detection and the estimation of the covered area A^sub c^. Even more, the area covered can be interpreted as a specific number of cells, allowing cell count for a given cell size.

From Fig. 5, it can be deduced that models of electrode-cell electrical performance can be used to derive the overlapping area in cell-electrode systems, useful for biological studies. It can be observed how the curve fits well with the frequency range, placing the maximum r value around 100 kHz, as predicted by FEM simulations [9, 10]. A value of R^sub gap^ = 90 kD was selected for this curve, representing a maximum value of the r curve with ff= 0.69, which represents the ratio (AJA), for a cell size of 30 µm diameter showed at figure obtained using FEM simulations [10]. Impedance sensor curves at Figs. 4 and 5 were obtained using SpectreHDL [15] mixed-mode simulator, with Analog Hardware Description Language (AHDL) for circuits in Fig. 3. An advantage of using AHDL models is the possibility of including non-linear performance of circuit elements, in our case, the frequency squared-root function at the Warburg impedance.

4. Cell Culture Applications

4.1. Electrode Model

The proposed model in Fig. 3 has three main parameters: the electrode area (A), fill-factor (ff), and the resistance of the gap region (R^sub gap^). Technology data were included and simulation results obtained to model a commercial electrode: 8W10E, from Applied Biophysics [12]. It is composed by eight wells, each one containing ten circular gold microelectrodes of 250 µm diameter. Ten sensing electrodes, in parallel, were used for ei and only one common reference electrode is used, much larger than the sensing ones.

Fig. 6 represents the normalized impedance r expected for these electrodes. For R^sub gap^ = 22 kQ, the fill factor changes from electrodes without cells on top (ff= 0.1) to those fully covered (ff= 0.9). Values of R^sub gap^ can be used to match the models to observed performance. In Fig. 7, R^sub gap^ values were changed for ff= 0.9, observing large changes in r. Finally, the electrode area was also modified for R^sub gap^ = 22 kD and ff= 0.9, showing the results in Fig. 8. It can be observed that the optimal working frequency is close to the one proposed by the electrode manufacturer (around 4 kHz), and that electrode area covered by cells can be approximated by using the fill factor parameters. The performance curves obtained before can be used to fit experimental results to the proposed model and find relevant biometrie characteristics.

4.2. CeU Growth

Cell growth experiments in AA8 cell line have been conducted using 8Wl OE sensors. A similar setup to [8] was used. AA8 cells from Chinese hamster were seeded initially, in an approximated number of 5000, and growth was monitored during seven days. In Fig. 9a the impedance evolution of the experiment is shown. The impedance range is around 1220 ohm (380 ohm - 1600 ohm). Considering the initial cell number of 5000 as very low, we can take the initial impedance as the no-cell impedance value (Z^sub nc^). At t = 6000 min, the medium was changed, and the confluent phase was achieved at approximately t = 8500 min. The maximum experimental value given from eq. (1) is around r= 3.1, as illustrates Fig. 9b. We consider in our model that the electrodes are approximately fully covered by cells fox ff= 0.9. The value of Rgap that better fits is 22 kohm. System response corresponds to r-values illustrated in Fig. 6. From these curves, it can be obtained the fill factor at different times. Table 1 summarizes the relative normalized impedance values r at several times. Using Fig. 6 for the sensor response, the fill factor is calculated at every instant. For a well area of 0.8 cm^sup 2^, the maximum cell number goes from 0.8 × 10^sup 6^ to 1.6×10^sup 6^. Number of cells, noeu, in Table 1, is obtained from 0.8 × 10^sup 6^ expected final cell number. A value of Znc= 380 O for r calculus in eq. (1) was considered.

4.3. Dosimetry

Experiments to characterize the influence of several drugs in cell growth were performed. The objective was to prove that the proposed model allows counting the cell number at different doses. It was considered the AA8 cell line and six different doses of MG 132 for growth inhibition (from 0.2 µM to 50 µM). 8Wl OE sensors were also used to carry out the dosimetry experiments.

After 72 hours of normal cell growth, the medium was changed and the drug added at different doses: 0.2, 0.5, 1, 5, 10 and 50 µM for wells 3 to 8 respectively. Well 2 was the control. Measured impedances for the 8 wells are shown in Fig. 10, for 4 kHz working frequency. At the end of the experiment it can be observed that the impedance decreases as the drug doses increases. Control (W2) is full of cells with the maximum impedance, while the maximum dose (W8) has the lowest resistance, at the bottom. The black line (Wl) represents the electrode-solution impedance. After the medium changes (t = 4000 min), it is observed a decreasing impedance below the initial baseline level (400 ohm) that we cannot explain. Final impedance values at 8000 min, Z^sub c^, were considered, at Table 2. From Z^sub nc^ and Z^sub c^, r values are calculated in the third column. Using curves for r versus frequency in Fig. 6, the ff estimated values from proposed model are obtained. The cell number at the end of the experiment was also counted and shown at the last column for each well. Considering ff^sub max^ = 0.9 for a measured cell number of 8.06x10^sup 5^, the expected values for care calculated.

The same data are summarized in Table 3 for 2, 4 and 10 kHz frequencies respectively. The better agreement is obtained at 4 kHz in fill factor (ff). It is observed that the impedance baseline, Znc, for r calculus decreases with frequency probably due to electrode impedance dependence. For medium resistance (Wl) and high drug concentrations wells (W6-W8), the resistance measured is below ZMC, so eq. (1) cannot be applied for r calculation.

5. Conclusions

This work describes an area-dependent model for cell-electrode systems and its application to measure and identify cells during cell culture protocols. A practical circuit for electrode-solution-cell simulation was employed, using an AHDL description for commercial electrodes, obtaining a good matching. Optimal measurement frequency was identified near 4 kHz. A cell growth evolution study based on 8Wl OE electrode models is presented. Curves obtained experimentally allow the real time growth monitoring by fitting the Rgap parameter. An estimation of the number of cells was obtained by using sensor curves calculated from the electrical model proposed. Dosimetry experiments reproduce similar conditions to cell growth, but in this case, a growth inhibitor is added at different doses. A decreasing impedance is observed, below the baseline expected (Znc) that we cannot explain. However, for the control and small drug doses, impedance curves are perfectly aligned. A proposed model with Rgap = 22 kQ was fitted to explain experimental data. Deviations from data are over 10-20 % in fill factor, more accurate for 4 kHz.

The deviations in fill factors measured are not small, being required to analyze the influence of error sources to increase the system performance. First, Signal-to-Noise Ratio (SNR) should be increased at the setup. Second, the proposed model has the advantage that it only needs one parameter (Rgap), versus other reported models using three parameters [8]. One parameter model makes it easy to fit the experimental data, but it can introduce inaccuracy. The possibility to add more parameters to the model should be considered in the future.

Acknowledgements

Part of this work was carried out thanks the financial help from the project: "Auto-calibración y autotest en circuitos analógicos, mixtos y de radio frecuencia: Andalusian Government project PO-TIC-5386", co-financed with FEDER program. We also want to thank Citoquimica Ultraestructural Group (BIO 132) of Cell Biology Department, Biology Faculty, Seville University, for its valuable help in the lab to develop the cell culture experiments.